National 5 Maths practice questions by section

Original questions for every section, Paper 1 and Paper 2 style, with worked answers, and paper-style questions where each answer you type is checked.

Quick checks	Multiple choice, worked or timed
Paper-style questions	Paper 1 (no calculator) and Paper 2 (calculator)
Answers	Checked in any equivalent form, then the full working

Try 4 questions

Question 1Paper 1 style · no calculator

The graph shows the lines

y

= 2x - 1

and

x + y

= 5

. From the graph, solve the simultaneous equations

y

= 2x - 1

and

x + y

= 5

Question 2Paper 1 style · no calculator

In triangle

ABC

D

lies on

BC

and

AD

is perpendicular to

BC

AB

= 13

cm,

BD

= 5

cm and

DC

= 9

cm. Find the length of

AC

Question 3Paper 2 style · calculator

Find the magnitude of the vector

\begin{pmatrix} -5 \\ 8 \end{pmatrix}

, to 3 significant figures.

Question 4Paper 1 style · no calculator

The numbers of emails eleven office workers received in a morning were:

12, 15, 9, 20, 17, 14, 22, 11, 19, 16, 13

. Find the quartiles as the medians of the lower and upper halves of the ordered data, leaving out the median itself when the number of values is odd. Find the interquartile range.

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Questions people ask

How are typed answers checked?

By a maths checker that accepts equivalent forms: (x + 4)(2x - 3) counts for (2x - 3)(x + 4), and 3sqrt(2) counts as an exact surd, unless the question asks for one form.